title: Two algorithms for fitting constrained marginal models.
abstract: The two main algorithms that have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model, are studied in detail. It is shown that the updates produced by the two methods are identical, but that the Lagrangian method is more efficient in the case of identically distributed observations. A generalization is given of the regression algorithm for modelling the effect of exogenous individual-level covariates, a context in which the use of the Lagrangian algorithm would be infeasible for even moderate sample sizes. An extension of the method to likelihood-based estimation underL1-penalties is also considered.
authors.affiliation: Statistical Laboratory, University of Cambridge, UK.
authors.forename: R J
authors.initials: RJ
authors.lastname: Evans
authors.forename: A
authors.initials: A
authors.lastname: Forcina
keywords: L1-penalty; categorical data; marginal log-linear model; maximum likelihood; non-linear constraint